How can I make this surface in blender...?
There is basic support of NURBs surfaces in Blender. Basic is the keyword here. Check docs for detailed information about them: https://docs.blender.org/manual/en/dev/modeling/surfaces/introduction.html



In this example I've started with Surface NURBs Curve (marked as 1., red color) after moving and subdividing to achieve desired shape I've Duplicate it and made its reflection on X axis - S>X>-1. Than I've selected both Curves and made a segment - F. After some more tweaking individual vertices, subdividing surface and selecting Endpoint on V this is a result. 

Also I've added Subdivision Surface Modifier.

In conclusion, it is possible, but it's really painful in Blender as it is lacking many mesh modeling tools. Read the docs and maybe you will be happy with them.